Optical computers require microscopic optical switches to turn signals on and of

Question

Optical computers require microscopic optical switches to turn signals on and off. One device for doing so, which can be implemented in an integrated circuit, is the Mach-Zender interferometer seen in the figure(Figure 1). Light from an on-chip infrared laser (lambda = 1.070 ) is split into two waves that travel equal distances around the arms of the interferometer. One arm passes through an electro-optic crystal, a transparent material that can change its index of refraction in response to an applied voltage. Suppose both arms are exactly the same length and the crystal's index of refraction with no applied voltage is also 1.559.What is the first index of refraction of the electro-optic crystal larger than 1.559 that changes the optical switch to the state opposite the state you found in part a? I posted part a of this question as well.

Explanation / Answer

So the trick here is that one beam of the laser has to pass through the high refractive index (RI) crystal. This crystal will keep the wavelength the same while slowing down the wave(altering its phase in the material). This slowing down of the wave will alter its phase causing either constructive or destructive interference when they are recombined. The RI is equal to (original wave speed)/(new wave speed) therefore, new wave speed = original wave speed/1.559 and the original wave speed = speed of light = 3E8 m/s new wave speed = 1.92E8 m/s Thats a difference in (3E8-1.92E8)m/s = 1.07E8 m/s using the length of the crystal: 6.7E-6m*(1s/1.07E8 m) = 6.23E-14 sec of delay in the waveforms This needs to then be compared to the time of 1 period: Original wave speed = frequency* wavelength therefore, frequency = (3E8 m/s )/(1.070E-6 m) = 2.8E14 s^-1 period = 1/frequency = 1/2.8E14 = 3.57E-15 s taking the delay in the waveforms /period = 6.23E-14/3.57E-15 = 17.4673 that means the new wave will be 17.5 periods behind the original wave. Since it is 1/2 a period out of phase it will cause destructive interference making it dark. Please Rate :)

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